Bale wrapping devices for round balers are known. The pressed material, by way of example agricultural harvested material, but also paper or material residues, which has been shaped in round balers into round bales, is thereby wrapped with a wrapping material, by way of example net or foil. Bale wrapping devices of this kind are usually provided with a supply mechanism for introducing the wrapping material into a pressing chamber of the round baler, wherein the supply mechanism in a supply movement draws the wrapping material off from a supply reel and introduces it into an arranged supply opening of the pressing chamber. The supply reel is as a rule charged with a certain pretensioning force by a contact pressure device so that the wrapping material can be wrapped around the bale with a corresponding tension. The supply reel is mounted at a supply chamber formed on the frame of the baler and has to be replaced when the wrapping material has been used up. Replacing the reel takes place with a relatively high effort since on the one hand the weight of the supply reel has to be managed and on the other hand the pressing device has to be released from the power means acting with a controlling torque on the pressing device, or it is necessary to work against the controlling torque which is acting on the pressing device. It is therefore endeavoured to simplify and make more user friendly the replacement process for the supply reel.